Question: Simplify the following expression: $k = \dfrac{a^2 - a - 56}{a + 7} $
First factor the polynomial in the numerator. $ a^2 - a - 56 = (a + 7)(a - 8) $ So we can rewrite the expression as: $k = \dfrac{(a + 7)(a - 8)}{a + 7} $ We can divide the numerator and denominator by $(a + 7)$ on condition that $a \neq -7$ Therefore $k = a - 8; a \neq -7$